Approaching infinite temperature upon repeated measurements of a quantum system

J. Yi, P. Talkner, and G.-L. Ingold

Phys. Rev. A 84, 032121 (2011) DOI: 10.1103/PhysRevA.84.032121

The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied as a function of the time lag τ between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponential in the case of finite Hilbert space dimension. The rate characterizing this approach undergoes a sharp transition from a monotonically increasing to an erratically varying function of the time between subsequent measurements.